A status, on an Opportunity or Problem, is used to track its progress through certain steps from start to finish. These statuses can be set to have a Task required, which means that a user of the CRM has to take ownership of the record.
To change a status, simply open the required record, in the example below we are on an Opportunity, and select the 'Current Status' option.
This will give you a list of all the available statuses to choose from. Simply select the required one.